Sunday, March 6, 2011

Winning at Rock-Paper-Scissors

The New York Times has a web program that let’s you play Rock-Paper-Scissors online. The interesting thing about this game is that it can be shown that the most efficient strategy is to to play a completely random game. If you don’t play a random game, then your opponent can estimate your strategy and eventually begin to predict your moves. This is the idea behind the the New York Times game, which is frustratingly difficult to beat.

The concept in developing a good R-P-S strategy is to understand that it is difficult for humans to select a truly random sequence. There is a natural tendency to favor some choices, or avoid some choices or think that long runs of a choice should not occur, so that the chance of a repeat of the last choice goes down the longer the prior run. In a random process, the chance of particular choice (e.g. Rock) is independent of how many Rock choices have been made in the past run. There are all sorts of other subtleties that are discussed by the R-P-S community (yes, there is such a thing together with organized competition). These include:

Men tend to lead with Rock

People who know how to play R-P-S, know rule 1, so they tend to lead with paper

Women tend to lead with scissors.

Scissors is chosen less than the others, on average

People tend to switch to the last move that beat them.

and so on….

Thus if you can estimate the probability that a player is following a a non-random strategy, then you can develop a winning strategy. Of course by developing a winning strategy, your opponent can theoretically figure out a strategy to beat you. This sort of recursiveness could go on forever….